Question: Simplify the following expression: $q = \dfrac{-30t}{30t + 65}$ You can assume $t \neq 0$.
Answer: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-30t = - (2\cdot3\cdot5 \cdot t)$ The denominator can be factored: $30t + 65 = (2\cdot3\cdot5 \cdot t) + (5\cdot13)$ The greatest common factor of all the terms is $5$ Factoring out $5$ gives us: $q = \dfrac{(5)(-6t)}{(5)(6t + 13)}$ Dividing both the numerator and denominator by $5$ gives: $q = \dfrac{-6t}{6t + 13}$